Its usual a standard arras type of contract and if you speak spanish you should be fine.
Whilst many people do not engange a lawyer there is a paper trail after the event to look out for and a gestor can sometimes be very useful, but if you are well versed with procedure you should be fine!
If you are worried you could ask the buyers lawyer to handle the transaction for a small fee!!!
And yes it is a conflict of interest seemingly but dont forget the Notary has final say – ps you could contact the notary office as well and they will advise you!